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Question

If y=1x1+x then find (1x2)dydx+y =

A
1
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B
1
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C
2
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D
0
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Solution

The correct option is D 0
y=1x1+x
y2=1x1+x
y.y=(1+x)(1)(1x)(1)(1+x)2
y.y=1x1+x(1+x)2
yy=2(1+x)2
ydydx=2(1+x)2
dydx=2y(1+x)2
Given
(1x2)(dydx)+y
=(1x2)2y(1+x)2+y
=(1x)(1+x)+y
=(1(1x)(1+x).1y2)
=y(1(1x)(1+x)×1+x1x)
=0

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